What is the greatest number that, when it divides 1128, 1537 and 1834 leaves remainders 7, 3 and 5, respectively?
Given:
Numbers: 1128, 1537, 1834
Remainders: 7, 3, 5 respectively
Formula Used:
Required greatest number (N) = HCF of (1128 - 7, 1537 - 3, 1834 - 5)
Solution:
Subtract remainders from the numbers
1128 - 7 = 1121
1537 - 3 = 1534
1834 - 5 = 1829
HCF of 1121, 1534, and 1829
Prime factorization:
1121 = 59 × 19
1534 = 2 × 13 × 59
1829 = 31 × 59
=> The greatest number = 59
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What is the greatest number that, when it divides 1128, 1537 and 1834 leaves remainders 7, 3 and 5, respectively?
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